Daily Practice · Higher Plus
June 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2000 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2000f(x) = 2x + 4. Work out the inverse function f^-1(x).
- 2nd June 2000A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd June 2000A cuboid measures 12 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th June 2000A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th June 2000A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 6th June 2000Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 7th June 2000Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 8th June 2000y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 9th June 2000The 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.
- 10th June 2000A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 11th June 2000On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th June 2000A block has mass 830 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th June 2000Use the iteration x(n+1) = cube root of (7x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 14th June 2000y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 15th June 2000In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 16th June 2000The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 17th June 2000A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 18th June 2000x = 173 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th June 2000Work out the nth term of the quadratic sequence 11, 19, 31, 47, ...
- 20th June 2000y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 4.
- 21st June 2000In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 22nd June 2000A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 23rd June 2000On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th June 2000A car covers 180 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.
- 25th June 2000The point (-3, 6) lies on y = f(x). Write down its image on y = f(x) - 1.
- 26th June 2000A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 27th June 2000A cuboid measures 14 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th June 2000A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th June 2000A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 30th June 2000Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.