Daily Practice · Higher Plus
July 1986 5-a-day
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The batch download puts all 5 tiers' July 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1986A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 2nd July 1986A rectangle is 10 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd July 1986Work out the nth term of the quadratic sequence 3, 8, 19, 36, ...
- 4th July 1986y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 5th July 1986In a vector proof you find that vector PQ = 2a + 5b and vector RS = 10a + 25b. What does this show about PQ and RS?
- 6th July 1986A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 7th July 1986On 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?
- 8th July 1986Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 9th July 1986The point (3, -4) lies on y = f(x). Write down its image on y = f(x) + 3.
- 10th July 1986y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 11th July 1986A cuboid measures 9 cm by 8 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th July 1986A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th July 1986A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 14th July 1986A block has mass 740 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th July 1986Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 16th July 1986y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 49.
- 17th July 1986A cuboid measures 9 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th July 1986A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th July 1986On 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?
- 20th July 1986x = 89 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st July 1986f(x) = 4x + 3 and g(x) = 3x - 2. Work out fg(1).
- 22nd July 1986A train slows steadily from 34 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd July 1986The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 24th July 1986A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 25th July 1986A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 26th July 1986A car covers 190 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.
- 27th July 1986The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 28th July 1986y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 29th July 1986In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 30th July 1986The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 31st July 1986On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?