Daily Practice · Higher Plus
October 1981 5-a-day
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The batch download puts all 5 tiers' October 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd October 1981Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 3rd October 1981Work out the nth term of the quadratic sequence 4, 11, 26, 49, ...
- 4th October 1981A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 5th October 1981A cuboid measures 11 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th October 1981A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th October 1981A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 8th October 1981Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
- 9th October 1981The point (1, 5) lies on y = f(x). Write down its image on y = f(x) - 1.
- 10th October 1981y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 11th October 1981A cuboid measures 6 cm by 6 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th October 1981A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th October 1981On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th October 1981A rectangle is 27 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th October 1981Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 16th October 1981y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 17th October 1981The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 18th October 1981A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 19th October 1981A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 20th October 1981Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 21st October 1981f(x) = 6x - 3 and g(x) = 5x + 3. Work out fg(5).
- 22nd October 1981y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 64.
- 23rd October 1981In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 24th October 1981The probability of winning a game is 7/10. A player expects 14 wins. How many games did they play?
- 25th October 1981On 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?
- 26th October 1981A block has mass 740 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th October 1981The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 28th October 1981A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 29th October 1981In a vector proof you find that vector PQ = 6a + 2b and vector RS = 18a + 6b. What does this show about PQ and RS?
- 30th October 1981A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 31st October 1981A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?