Daily Practice · Higher Plus
June 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1995 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1995A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd June 1995On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd June 1995A car covers 690 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th June 1995Use the iteration x(n+1) = cube root of (11x(n) + 1) with x(0) = 2. Work out x(1) to 3 decimal places.
- 5th June 1995A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 6th June 1995The 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.
- 7th June 1995A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 8th June 1995A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 9th June 1995Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 10th June 1995Work out the nth term of the quadratic sequence 5, 15, 31, 53, ...
- 11th June 1995y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 12th June 1995In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 13th June 1995The probability of winning a game is 1/2. A player expects 70 wins. How many games did they play?
- 14th June 1995On 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?
- 15th June 1995Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 16th June 1995The point (6, 1) lies on y = f(x). Write down its image on y = f(x - 1).
- 17th June 1995y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 18th June 1995In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 19th June 1995A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 20th June 1995A 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?
- 21st June 1995A rectangle is 5 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd June 1995Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 23rd June 1995y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 25.
- 24th June 1995A cuboid measures 5 cm by 11 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th June 1995A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th June 1995On 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?
- 27th June 1995Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 28th June 1995f(x) = 5x + 3 and g(x) = 3x - 7. Work out fg(0).
- 29th June 1995A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 30th June 1995A cuboid measures 13 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.