Daily Practice · Higher Plus
June 1985 5-a-day
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The batch download puts all 5 tiers' June 1985 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1985A car covers 230 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 June 1985Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 3rd June 1985y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 81.
- 4th June 1985In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 5th June 1985The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 6th June 1985On 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?
- 7th June 1985Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 8th June 1985f(x) = 2x - 2 and g(x) = 3x + 1. Work out fg(-3).
- 9th June 1985A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 10th June 1985In a vector proof you find that vector PQ = 5a + 2b and vector RS = 25a + 10b. What does this show about PQ and RS?
- 11th June 1985A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 12th June 1985A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 13th June 1985Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 14th June 1985The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 15th June 1985y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 16th June 1985A cuboid measures 6 cm by 8 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th June 1985A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th June 1985On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th June 1985A rectangle is 12 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th June 1985A quadratic sequence starts -5, -4, -1, 4. Work out the second difference, and the coefficient of n^2.
- 21st June 1985y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 22nd June 1985A cuboid measures 7 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd June 1985A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th June 1985A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 25th June 1985Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 26th June 1985Solve x^2 + 6x - 7 > 0.
- 27th June 1985y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 9.
- 28th June 1985The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 29th June 1985A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 30th June 1985On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?