Daily Practice · Higher Plus
April 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2001 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2001A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 2nd April 2001A block has mass 290 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd April 2001f(x) = 8x + 7. Work out the inverse function f^-1(x).
- 4th April 2001y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 81.
- 5th April 2001The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 6th April 2001A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 7th April 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 8th April 2001x = 64 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th April 2001Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 10th April 2001A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 11th April 2001In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 12th April 2001The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 13th April 2001A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 14th April 2001A car covers 660 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th April 2001Use the iteration x(n+1) = cube root of (5x(n) + 7) with x(0) = 2. Work out x(1) to 3 decimal places.
- 16th April 2001y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 17th April 2001In a vector proof you find that vector PQ = 2a + 2b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 18th April 2001A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 19th April 2001On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th April 2001Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 21st April 2001Work out the nth term of the quadratic sequence -9, -10, -9, -6, ...
- 22nd April 2001y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 23rd April 2001A cuboid measures 15 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th April 2001A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th April 2001A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 26th April 2001Simplify sqrt(72) + sqrt(32), giving your answer in the form a sqrt(b).
- 27th April 2001The point (0, 5) lies on y = f(x). Write down its image on y = f(x + 2).
- 28th April 2001y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 25.
- 29th April 2001A cuboid measures 6 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th April 2001A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?