Daily Practice · Higher Plus
August 1961 5-a-day
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The batch download puts all 5 tiers' August 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1961Solve 12x^2 - 19x + 5 = 0.
- 2nd August 1961A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd August 1961The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 4th August 1961A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 5th August 1961A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 6th August 1961x = 189 and y = 74, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th August 1961f(x) = 8x - 7. Work out the inverse function f^-1(x).
- 8th August 1961y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 9th August 1961In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 10th August 1961The probability of winning a game is 1/8. A player expects 2 wins. How many games did they play?
- 11th August 1961On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th August 1961A car covers 410 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.
- 13th August 1961Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 14th August 1961y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 15th August 1961In a vector proof you find that vector PQ = 3a + b and vector RS = 6a + 2b. What does this show about PQ and RS?
- 16th August 1961A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 17th August 1961A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 18th August 1961Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 19th August 1961Use the iteration x(n+1) = cube root of (7x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 20th August 1961y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 25.
- 21st August 1961A cuboid measures 9 cm by 9 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd August 1961A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd August 1961On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th August 1961Simplify sqrt(80) + sqrt(180), giving your answer in the form a sqrt(b).
- 25th August 1961Work out the nth term of the quadratic sequence 8, 18, 34, 56, ...
- 26th August 1961A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 27th August 1961A cuboid measures 7 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th August 1961A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th August 1961A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 30th August 1961A rectangle is 9 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st August 1961The point (-5, 0) lies on y = f(x). Write down its image on y = f(-x).