Daily Practice · Higher Plus
April 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1958 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1958f(x) = 2x + 5. Work out the inverse function f^-1(x).
- 2nd April 1958y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 3rd April 1958In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
- 4th April 1958A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 5th April 1958On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th April 1958x = 108 and y = 79, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th April 1958Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 8th April 1958y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 9th April 1958A cuboid measures 14 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th April 1958A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th April 1958A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 12th April 1958A car covers 820 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th April 1958Use the iteration x(n+1) = cube root of (5x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 14th April 1958y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
- 15th April 1958A cuboid measures 5 cm by 9 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th April 1958A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th April 1958On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th April 1958Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 19th April 1958Work out the nth term of the quadratic sequence -6, -3, 4, 15, ...
- 20th April 1958A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 21st April 1958The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 22nd April 1958A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 23rd April 1958A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 24th April 1958Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 25th April 1958The point (-1, -6) lies on y = f(x). Write down its image on y = f(x + 4).
- 26th April 1958y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 27th April 1958In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 28th April 1958The probability of winning a game is 3/10. A player expects 6 wins. How many games did they play?
- 29th April 1958On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th April 1958A rectangle is 7 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.