**New for 2019!** I have completed the 2018 ENGAA Section 1 within the time limit and have given some of my techniques and strategies for achieving this below.

I recommend that you take the exam whilst being well rested and well practised without a lot of last minute preparation. I made some mistakes and slowed down considerably towards the end of the paper - it will be difficult to avoid this if you cram and don't get enough sleep/rest.

You may have encountered advice to move on from a question after a certain amount of time (just under 1 minute 29 seconds) no matter how much progress you have made in it. I believe this to be poor advice - the questions vary in difficulty and my shortest question took just 15 seconds.

I recommend writing as little as possible and use a pencil throughout (including in your practice attempts) so you don't have to change to mark the answers.

Please contact me if you have any queries or would like advice on achieving optimal preparation to reduce unforced errors.

Question 1 - 0:57

Question 2 - 0:29

Question 3 - 0:39

Question 4 - 0:44

Question 5 - 0:46

Question 6 - 1:13

Question 7 - 1:13

Question 8 - 0:49

Question 9 - 0:48

Question 10 - 1:17

Question 11 - 1:09

Question 12 - 0:34

Question 13 - 1:27

Question 14 - 0:35

Question 15 - 0:54

Question 16 - 1:00

Question 17 - 0:59

Question 18 - 0:40

Question 19 - 1:33

Question 20 - 1:43

Question 21 - 0:48

Question 22 - 1:20

Question 23 - 1:51

Question 24 - 1:14

Question 25 - 0:39

Question 26 - 2:24

Question 27 - 2:00

Question 28 - 2:33

Question 29 - 1:01

Question 30 - 0:36

Question 31 - 0:31

Question 32 - 0:36

Question 33 - 0:42

Question 34 - 0:56

Question 35 - 2:41

Question 36 - 0:56

Question 37 - 0:57

Question 38 - 1:23

Question 39 - 1:39

Question 40 - 0:51

Question 41 - 0:15

Question 42 - 1:23

Question 43 - 1:33

Question 44 - 2:06

Question 45 - 2:11

Question 46 - 1:13

Question 47 - 0:18

Question 48 - 0:57

Question 49 - 1:39

Question 50 - 0:35

Question 51 - 1:22

Question 52 - 0:46

Question 53 - 15:38

Question 54 - 1:00

Total - 75:59

Question 1 - 0:57 CORRECT (E)

Question 2 - 0:29 CORRECT (B)

$-10$

Question 3 - 0:39 INCORRECT (Answer marked - D but should have been B. I multiplied by two because the faces of cuboids come in pairs and this factor of two 'interfered' with the doubling of the surface area in my mind leading to me omitting to double the surface area)

$2\sqrt2x^3=2(2+2\sqrt2+\sqrt2)x^2$

$x=\frac{2}{\sqrt2}+3$

Question 4 - 0:44 CORRECT (B)

$V=\frac{12+15+3}{5}=6$

$I=\frac{6}{27}=\frac{2}{9}$

Question 5 - 0:46 CORRECT (H)

$\frac{2p-(p-1)}{1-2p}=\frac{-2}{3}$

$3p+3=-2+4p$

Question 6 - 1:13 CORRECT (G)

$f=\frac{c}{\lambda}=\frac{3\times 10^8}{400\times 10^{-9}}=0.75\times 10^{15}=7.5\times 10^{14}$

Question 7 - 1:13 CORRECT (D)

$2x^2=96$

$x=\sqrt{48}$

$r=\frac{\sqrt5x}{2}$

$\sqrt5\sqrt{12}$

Question 8 - 0:49 CORRECT (E)

$\frac{95}{100}\times 100\times 60\times 10$

$60000-$

Question 9 - 0:48 CORRECT (E)

$\frac{320}{4^3}\times 5^3$

Question 10 - 1:17 CORRECT (C)

Look for cancellation by a factor of 100 then only work out the first digit of your answer to be 9 - don't spend time worrying about the number of zeros.

Question 11 - 1:09 CORRECT (C)

Use 1/2 b*h with a vertical base and the height is the x co-ordinate of the intersection of the slanted lines.

Question 12 - 0:34 INCORRECT (Answer marked - B but should have been A. Numerical slip)

Write equations and don't bother to work out 2*96.

Question 13 - 1:27 CORRECT (E)

Cancel zeros and factors of 4 as much as possible.

Question 14 - 0:35 CORRECT (A)

If there is a table of answers I put a vertical line alongside those which are correct (for instance in this example when you realise that the background count is 20 I recommend putting a vertical line next to answers A-D). You can do this without stopping thinking about the question.

Question 15 - 0:54 CORRECT (D)

Write the minimum of angles on the diagram and divide 180 and 48 by 2 individually if it helps.

Question 16 - 1:00 CORRECT (C)

Draw a simple free body diagram and rearrange the equation without writing the last step(s).

Question 17 - 0:59 CORRECT (C)

Use the percentage multiplier method. It helped to know that 0.6=3/5 and that 15^2=225.

Question 18 - 0:40 INCORRECT (Answer marked - D but should have been E. I doubled the amplitude, failing to visualise that it would be quadrupled for an entire cycle)

Write the minimum of working.

Question 19 - 1:33 CORRECT (E)

Draw a rough diagram taking advantage of alternate angles.

Question 20 - 1:43 CORRECT (C)

Work out the volume of the water without writing too much and use this to determine the mass of the measuring cylinder.

Question 21 - 0:48 CORRECT (C)

Apply circle theorems directly to the diagram.

Question 22 - 1:20 CORRECT (B)

Choose convenient points to work out the gradient of the line. Spot/know that 0.4*2.5=1.

Question 23 - 1:51 CORRECT (C)

When you reach an equation which only involves the base of the triangle, try to solve it by inspection.

Question 24 - 1:14 CORRECT (H)

The number of neutrons can be worked out as even or odd rather than the exact number if this helps.

Question 25 - 0:39 INCORRECT (Answer marked - G but should have been A. I forgot that q was negative when subtracting it from/adding it to p)

Try to get the nth term by inspection.

Question 26 - 2:24 CORRECT (C)

Work out what V^2/R is from the information given then work out what is required in terms of V^2/R.

Question 27 - 2:00 CORRECT (B)

It is better to work out the probability of 0 or 1 green sweets being taken and subtract this from 1 rather than work out the probability of taking more than 1 green sweet directly.

Question 28 - 2:33 CORRECT (A)

Draw a rough diagram and be confident about your conclusions - I spent too long making sure I was correct.

Question 29 - 1:01 CORRECT (A)

Keep your diagram rough and integrate from 0 to 2 whilst doubling.

Question 30 - 0:36 CORRECT (E)

Cancel zeros and write the absolute minimum towards the end of the question.

Question 31 - 0:31 CORRECT (D)

Don't overlook that sin(theta)=0 is a solution. I prefer drawing the graphs to CAST diagrams or mnemonics.

Question 32 - 0:36 CORRECT (F)

Make your first scan of the answers brief - upon seeing F it should be clear this is the answer. It is probably no accident that it appears near the end of the list rather than the start.

Question 33 - 0:42 INCORRECT (Answer marked - C but should have been A. Slip in remembering the condition for a zero discriminant (b^2-4ac=0))

Question 34 - 0:56 CORRECT (D)

Calculate the overall acceleration then work from the left.

Question 35 - 2:41 CORRECT (D)

Work in radians throughout and accept that this is a trickier question so may take longer than others.

Question 36 - 0:56 CORRECT (F)

If you reach 1400/4 you may find it easier to divide by 2 twice rather than directly by 4.

Question 37 - 0:57 CORRECT (E)

Try to rearrange the equation from the second bullet point in your head to give a=2d+1

Question 38 - 1:23 CORRECT (B)

Try to realise quickly that the potential appears on the numerator and as the denominator which allows for a cancellation to give 1.

Question 39 - 1:39 CORRECT (B)

Start by writing an equation involving writing the common ratio in two different ways. Simplify the common ratio to 3 then work out 6*3^4 quickly while looking at the answers.

Question 40 - 0:51 CORRECT (D)

If possible, write equations with the numbers already substituted in e.g. 24=5v instead of m1v1=m2v2.

Question 41 - 0:15 CORRECT (C)

Spot that when the logarithms are combined there are many cancellations leading to log to base 2 of 64/4.

Question 42 - 1:23 CORRECT (G)

Write the energy gains and losses preferably with numbers immediately from the first step.

Question 43 - 1:33 CORRECT (C)

Spot that sqrt(80)=4sqrt(5)

Question 44 - 2:06 CORRECT (F)

Do an efficient conservation of momentum calculation which reveals that Sphere Y is always travelling in the negative direction.

Question 45 - 2:11 CORRECT (D)

If you have difficulty factorising the quadratic then look at the answers.

Question 46 - 1:13 CORRECT (A)

Ignore the vertical direction.

Question 47 - 0:18 CORRECT (D)

Use difference of two squares to notice that this expansion will only consist of even powers.

Question 48 - 0:57 CORRECT (A)

Spot a familiar triangle.

Question 49 - 1:39 CORRECT (E)

Try to integrate on sight then dividing the resulting equations eliminates the cumbersome 2^m.

Question 50 - 0:35 CORRECT (E)

A quick conservation of momentum calculation whilst being confident about your answer - there are no hidden difficulties here.

Question 51 - 1:22 CORRECT (A)

Integrate the first equation in your head and rearrange the third one to give f(4)-f(2)=18 and substitute this in immediately for the integral of the LHS of the first equation.

Question 52 - 0:46 CORRECT (F)

Divide the potential energy by 2 from the outset.

Question 53 - 15:38 CORRECT (C)

This question took a long time, partly because I was getting tired but also nervous. I also went the wrong way to begin with by looking for a solution in integers but should have realised from the outset that a differentiation would be involved. Once I corrected my approach I made several numerical slips.

Question 54 - 1:00 CORRECT (B)

Use the first object to work out the time taken for its flight, solving equations by inspection where possible.

Total - 75:59 plus checking time

49 CORRECT 5 INCORRECT

Look for cancellation by a factor of 100 then only work out the first digit of your answer to be 9 - don't spend time worrying about the number of zeros.

Question 11 - 1:09 CORRECT (C)

Use 1/2 b*h with a vertical base and the height is the x co-ordinate of the intersection of the slanted lines.

Question 12 - 0:34 INCORRECT (Answer marked - B but should have been A. Numerical slip)

Write equations and don't bother to work out 2*96.

Question 13 - 1:27 CORRECT (E)

Cancel zeros and factors of 4 as much as possible.

Question 14 - 0:35 CORRECT (A)

If there is a table of answers I put a vertical line alongside those which are correct (for instance in this example when you realise that the background count is 20 I recommend putting a vertical line next to answers A-D). You can do this without stopping thinking about the question.

Question 15 - 0:54 CORRECT (D)

Write the minimum of angles on the diagram and divide 180 and 48 by 2 individually if it helps.

Question 16 - 1:00 CORRECT (C)

Draw a simple free body diagram and rearrange the equation without writing the last step(s).

Question 17 - 0:59 CORRECT (C)

Use the percentage multiplier method. It helped to know that 0.6=3/5 and that 15^2=225.

Question 18 - 0:40 INCORRECT (Answer marked - D but should have been E. I doubled the amplitude, failing to visualise that it would be quadrupled for an entire cycle)

Write the minimum of working.

Question 19 - 1:33 CORRECT (E)

Draw a rough diagram taking advantage of alternate angles.

Question 20 - 1:43 CORRECT (C)

Work out the volume of the water without writing too much and use this to determine the mass of the measuring cylinder.

Question 21 - 0:48 CORRECT (C)

Apply circle theorems directly to the diagram.

Question 22 - 1:20 CORRECT (B)

Choose convenient points to work out the gradient of the line. Spot/know that 0.4*2.5=1.

Question 23 - 1:51 CORRECT (C)

When you reach an equation which only involves the base of the triangle, try to solve it by inspection.

Question 24 - 1:14 CORRECT (H)

The number of neutrons can be worked out as even or odd rather than the exact number if this helps.

Question 25 - 0:39 INCORRECT (Answer marked - G but should have been A. I forgot that q was negative when subtracting it from/adding it to p)

Try to get the nth term by inspection.

Question 26 - 2:24 CORRECT (C)

Work out what V^2/R is from the information given then work out what is required in terms of V^2/R.

Question 27 - 2:00 CORRECT (B)

It is better to work out the probability of 0 or 1 green sweets being taken and subtract this from 1 rather than work out the probability of taking more than 1 green sweet directly.

Question 28 - 2:33 CORRECT (A)

Draw a rough diagram and be confident about your conclusions - I spent too long making sure I was correct.

Question 29 - 1:01 CORRECT (A)

Keep your diagram rough and integrate from 0 to 2 whilst doubling.

Question 30 - 0:36 CORRECT (E)

Cancel zeros and write the absolute minimum towards the end of the question.

Question 31 - 0:31 CORRECT (D)

Don't overlook that sin(theta)=0 is a solution. I prefer drawing the graphs to CAST diagrams or mnemonics.

Question 32 - 0:36 CORRECT (F)

Make your first scan of the answers brief - upon seeing F it should be clear this is the answer. It is probably no accident that it appears near the end of the list rather than the start.

Question 33 - 0:42 INCORRECT (Answer marked - C but should have been A. Slip in remembering the condition for a zero discriminant (b^2-4ac=0))

Question 34 - 0:56 CORRECT (D)

Calculate the overall acceleration then work from the left.

Question 35 - 2:41 CORRECT (D)

Work in radians throughout and accept that this is a trickier question so may take longer than others.

Question 36 - 0:56 CORRECT (F)

If you reach 1400/4 you may find it easier to divide by 2 twice rather than directly by 4.

Question 37 - 0:57 CORRECT (E)

Try to rearrange the equation from the second bullet point in your head to give a=2d+1

Question 38 - 1:23 CORRECT (B)

Try to realise quickly that the potential appears on the numerator and as the denominator which allows for a cancellation to give 1.

Question 39 - 1:39 CORRECT (B)

Start by writing an equation involving writing the common ratio in two different ways. Simplify the common ratio to 3 then work out 6*3^4 quickly while looking at the answers.

Question 40 - 0:51 CORRECT (D)

If possible, write equations with the numbers already substituted in e.g. 24=5v instead of m1v1=m2v2.

Question 41 - 0:15 CORRECT (C)

Spot that when the logarithms are combined there are many cancellations leading to log to base 2 of 64/4.

Question 42 - 1:23 CORRECT (G)

Write the energy gains and losses preferably with numbers immediately from the first step.

Question 43 - 1:33 CORRECT (C)

Spot that sqrt(80)=4sqrt(5)

Question 44 - 2:06 CORRECT (F)

Do an efficient conservation of momentum calculation which reveals that Sphere Y is always travelling in the negative direction.

Question 45 - 2:11 CORRECT (D)

If you have difficulty factorising the quadratic then look at the answers.

Question 46 - 1:13 CORRECT (A)

Ignore the vertical direction.

Question 47 - 0:18 CORRECT (D)

Use difference of two squares to notice that this expansion will only consist of even powers.

Question 48 - 0:57 CORRECT (A)

Spot a familiar triangle.

Question 49 - 1:39 CORRECT (E)

Try to integrate on sight then dividing the resulting equations eliminates the cumbersome 2^m.

Question 50 - 0:35 CORRECT (E)

A quick conservation of momentum calculation whilst being confident about your answer - there are no hidden difficulties here.

Question 51 - 1:22 CORRECT (A)

Integrate the first equation in your head and rearrange the third one to give f(4)-f(2)=18 and substitute this in immediately for the integral of the LHS of the first equation.

Question 52 - 0:46 CORRECT (F)

Divide the potential energy by 2 from the outset.

Question 53 - 15:38 CORRECT (C)

This question took a long time, partly because I was getting tired but also nervous. I also went the wrong way to begin with by looking for a solution in integers but should have realised from the outset that a differentiation would be involved. Once I corrected my approach I made several numerical slips.

Question 54 - 1:00 CORRECT (B)

Use the first object to work out the time taken for its flight, solving equations by inspection where possible.

Total - 75:59 plus checking time

49 CORRECT 5 INCORRECT