Daily Practice · Higher Plus
July 1981 5-a-day
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The batch download puts all 5 tiers' July 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1981In a vector proof you find that vector PQ = 2a + 6b and vector RS = 6a + 18b. What does this show about PQ and RS?
- 2nd July 1981A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 3rd July 1981A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 4th July 1981A car covers 350 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th July 1981Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 6th July 1981y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 7th July 1981A cuboid measures 9 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th July 1981A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th July 1981On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th July 1981Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 11th July 1981f(x) = 5x - 3 and g(x) = 3x - 2. Work out fg(-3).
- 12th July 1981y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 13th July 1981A cuboid measures 13 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th July 1981A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th July 1981A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 16th July 1981Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 17th July 1981The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 18th July 1981y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 16.
- 19th July 1981The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 20th July 1981A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 21st July 1981On 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?
- 22nd July 1981A rectangle is 15 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd July 1981A quadratic sequence starts 11, 26, 49, 80. Work out the second difference, and the coefficient of n^2.
- 24th July 1981A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
- 25th July 1981In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 26th July 1981The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 27th July 1981A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 28th July 1981Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 29th July 1981Solve x^2 + 9x + 20 < 0.
- 30th July 1981y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 31st July 1981In a vector proof you find that vector PQ = 3a + 6b and vector RS = 15a + 30b. What does this show about PQ and RS?