Daily Practice · Higher Plus
April 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1959 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1959A rectangle is 19 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd April 1959Write x^2 + 2x - 4 in the form (x + a)^2 + b.
- 3rd April 1959y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 4th April 1959A cuboid measures 11 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th April 1959A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th April 1959A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 7th April 1959Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 8th April 1959Work out the coordinates of the turning point of y = x^2 + 12x + 9.
- 9th April 1959y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 10th April 1959A cuboid measures 10 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th April 1959A bag holds 6 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th April 1959On 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?
- 13th April 1959A block has mass 260 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th April 1959Simplify (x^2 + 13x + 42)/(x + 6).
- 15th April 1959A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 16th April 1959The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 17th April 1959A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 18th April 1959A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 19th April 1959x = 99 and y = 32, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th April 1959In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 21st April 1959y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 22nd April 1959In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 23rd April 1959The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 24th April 1959On 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?
- 25th April 1959A car covers 220 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.
- 26th April 1959Make x the subject of 6x + 2 = y(x + 2).
- 27th April 1959y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 28th April 1959In a vector proof you find that vector PQ = a + b and vector RS = 2a + 2b. What does this show about PQ and RS?
- 29th April 1959A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 30th April 1959A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?