Daily Practice · Higher Plus
July 1962 5-a-day
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The batch download puts all 5 tiers' July 1962 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1962On 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?
- 2nd July 1962A block has mass 460 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd July 1962The point (6, 5) lies on y = f(x). Write down its image on y = f(x - 1).
- 4th July 1962A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 5th July 1962In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 6th July 1962The probability of winning a game is 5/8. A player expects 35 wins. How many games did they play?
- 7th July 1962A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 8th July 1962x = 158 and y = 124, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th July 1962Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 10th July 1962y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 11th July 1962In a vector proof you find that vector PQ = 3a + 3b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 12th July 1962A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 13th July 1962On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th July 1962A car covers 660 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th July 1962f(x) = 6x - 7 and g(x) = 4x + 9. Work out fg(0).
- 16th July 1962y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 17th July 1962A cuboid measures 9 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th July 1962A 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?
- 19th July 1962A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 20th July 1962Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 21st July 1962The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 22nd July 1962y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 64.
- 23rd July 1962A cuboid measures 8 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th July 1962A bag holds 4 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th July 1962On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th July 1962Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 27th July 1962A quadratic sequence starts 9, 22, 43, 72. Work out the second difference, and the coefficient of n^2.
- 28th July 1962A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 29th July 1962The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 30th July 1962A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 31st July 1962A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?