Daily Practice · Higher Plus
July 1983 5-a-day
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The batch download puts all 5 tiers' July 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1983The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 2nd July 1983y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 3rd July 1983A cuboid measures 10 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th July 1983A bag holds 3 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th July 1983A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 6th July 1983A rectangle is 4 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th July 1983A quadratic sequence starts 11, 15, 21, 29. Work out the second difference, and the coefficient of n^2.
- 8th July 1983y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 49.
- 9th July 1983The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 10th July 1983A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 11th July 1983On 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?
- 12th July 1983Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 13th July 1983Solve x^2 + 4x + 3 > 0.
- 14th July 1983A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 15th July 1983In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 16th July 1983The probability of winning a game is 5/8. A player expects 55 wins. How many games did they play?
- 17th July 1983A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 18th July 1983A block has mass 430 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th July 1983Write x^2 + 10x + 4 in the form (x + a)^2 + b.
- 20th July 1983y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 21st July 1983In a vector proof you find that vector PQ = a + 5b and vector RS = 5a + 25b. What does this show about PQ and RS?
- 22nd July 1983A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 23rd July 1983On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th July 1983x = 136 and y = 32, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th July 1983Work out the coordinates of the turning point of y = x^2 - 12x + 6.
- 26th July 1983y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 27th July 1983A cuboid measures 9 cm by 10 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th July 1983A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th July 1983A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 30th July 1983A 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.
- 31st July 1983Simplify (x^2 + 10x + 16)/(x + 2).