Daily Practice · Higher Plus
April 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2000 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2000A car covers 510 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.
- 2nd April 2000The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 3rd April 2000y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 4th April 2000A cuboid measures 6 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th April 2000A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th April 2000A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 7th April 2000Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 8th April 2000A quadratic sequence starts 3, 10, 19, 30. Work out the second difference, and the coefficient of n^2.
- 9th April 2000y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 10th April 2000The 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.
- 11th April 2000A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 12th April 2000On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th April 2000Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 14th April 2000Solve x^2 - 3x - 10 > 0.
- 15th April 2000A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 16th April 2000In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 17th April 2000The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 18th April 2000A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 19th April 2000A rectangle is 21 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th April 2000Write x^2 + 4x + 14 in the form (x + a)^2 + b.
- 21st April 2000y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 22nd April 2000In a vector proof you find that vector PQ = a + 6b and vector RS = 2a + 12b. What does this show about PQ and RS?
- 23rd April 2000A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 24th April 2000On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th April 2000Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 26th April 2000Work out the coordinates of the turning point of y = x^2 - 10x + 1.
- 27th April 2000y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 28th April 2000A cuboid measures 8 cm by 3 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th April 2000A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th April 2000A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?