Daily Practice · Higher Plus
April 1961 5-a-day
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The batch download puts all 5 tiers' April 1961 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1961On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd April 1961x = 109 and y = 6, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd April 1961In an algebraic proof, how would you write an odd number in terms of an integer n?
- 4th April 1961A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 5th April 1961The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 6th April 1961A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 7th April 1961A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 8th April 1961A car covers 470 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th April 1961Make x the subject of 7x + 8 = y(x + 8).
- 10th April 1961y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 11th April 1961In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 12th April 1961The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
- 13th April 1961On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th April 1961Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 15th April 1961Write 4/(x + 2) + 5/(x - 2) as a single fraction.
- 16th April 1961y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 17th April 1961In a vector proof you find that vector PQ = 3a - 2b and vector RS = 6a - 4b. What does this show about PQ and RS?
- 18th April 1961A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 19th April 1961A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 20th April 1961Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 21st April 1961Solve 8x^2 - 14x + 3 = 0.
- 22nd April 1961y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 23rd April 1961A cuboid measures 13 cm by 13 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th April 1961A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th April 1961On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th April 1961A rectangle is 9 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th April 1961f(x) = 8x - 9. Work out the inverse function f^-1(x).
- 28th April 1961A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 29th April 1961A cuboid measures 12 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th April 1961A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?