Daily Practice · Higher Plus
July 1985 5-a-day
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The batch download puts all 5 tiers' July 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1985A block has mass 260 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd July 1985Write x^2 + 6x + 2 in the form (x + a)^2 + b.
- 3rd July 1985A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 4th July 1985In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 5th July 1985The probability of winning a game is 9/10. A player expects 81 wins. How many games did they play?
- 6th July 1985A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 7th July 1985x = 87 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th July 1985Work out the coordinates of the turning point of y = x^2 + 2x + 12.
- 9th July 1985y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 10th July 1985In a vector proof you find that vector PQ = 2a - 6b and vector RS = 8a - 24b. What does this show about PQ and RS?
- 11th July 1985A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 12th July 1985On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th July 1985A car covers 810 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.
- 14th July 1985Simplify (x^2 - x - 12)/(x + 3).
- 15th July 1985y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 16th July 1985A cuboid measures 8 cm by 7 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th July 1985A 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?
- 18th July 1985A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 19th July 1985Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 20th July 1985In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 21st July 1985y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 81.
- 22nd July 1985A cuboid measures 11 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd July 1985A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th July 1985On 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?
- 25th July 1985Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 26th July 1985Make x the subject of 4x + 2 = y(x + 2).
- 27th July 1985A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 28th July 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 July 1985A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 30th July 1985A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 31st July 1985A rectangle is 26 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.