Daily Practice · Higher Plus
June 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1972 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1972A bag holds 7 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd June 1972On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd June 1972A car covers 520 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th June 1972In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 5th June 1972A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 6th June 1972The 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.
- 7th June 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 8th June 1972A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 9th June 1972Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 10th June 1972Make x the subject of 2x + 4 = y(x + 4).
- 11th June 1972y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 12th June 1972In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 13th June 1972The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
- 14th June 1972On 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?
- 15th June 1972Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 16th June 1972Write 5/(x + 6) + 2/(x - 5) as a single fraction.
- 17th June 1972y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 18th June 1972In a vector proof you find that vector PQ = 2a - 3b and vector RS = 4a - 6b. What does this show about PQ and RS?
- 19th June 1972A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th June 1972A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 21st June 1972A rectangle is 30 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd June 1972Solve 8x^2 - 14x - 15 = 0.
- 23rd June 1972y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 64.
- 24th June 1972A cuboid measures 7 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th June 1972A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th June 1972On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th June 1972Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 28th June 1972f(x) = 3x + 1. Work out the inverse function f^-1(x).
- 29th June 1972A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
- 30th June 1972A cuboid measures 6 cm by 14 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.