Daily Practice · Higher Plus
August 1960 5-a-day
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The batch download puts all 5 tiers' August 1960 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1960y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 16.
- 2nd August 1960A cuboid measures 14 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd August 1960A bag holds 6 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th August 1960On 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?
- 5th August 1960Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 6th August 1960The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 7th August 1960A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 8th August 1960The 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.
- 9th August 1960A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 10th August 1960A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 11th August 1960Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
- 12th August 1960A quadratic sequence starts 14, 24, 38, 56. Work out the second difference, and the coefficient of n^2.
- 13th August 1960y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 14th August 1960In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 15th August 1960The probability of winning a game is 9/10. A player expects 54 wins. How many games did they play?
- 16th August 1960On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th August 1960A rectangle is 15 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th August 1960Solve x^2 + x - 6 > 0.
- 19th August 1960y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 20th August 1960In a vector proof you find that vector PQ = 6a + 5b and vector RS = 30a + 25b. What does this show about PQ and RS?
- 21st August 1960A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 22nd August 1960A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 23rd August 1960Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 24th August 1960Write x^2 - 6x + 10 in the form (x + a)^2 + b.
- 25th August 1960y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 64.
- 26th August 1960A cuboid measures 12 cm by 13 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th August 1960A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th August 1960On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th August 1960A block has mass 220 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th August 1960Work out the coordinates of the turning point of y = x^2 - 12x + 13.
- 31st August 1960A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.