Daily Practice · Higher Plus
August 1967 5-a-day
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The batch download puts all 5 tiers' August 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1967y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 2nd August 1967The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 3rd August 1967A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 4th August 1967On 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?
- 5th August 1967A car covers 850 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th August 1967A quadratic sequence starts 13, 22, 33, 46. Work out the second difference, and the coefficient of n^2.
- 7th August 1967y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 8th August 1967In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 9th August 1967The probability of winning a game is 2/5. A player expects 20 wins. How many games did they play?
- 10th August 1967A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 11th August 1967Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 12th August 1967Solve x^2 + 6x + 8 < 0.
- 13th August 1967y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 4.
- 14th August 1967In a vector proof you find that vector PQ = 2a + 5b and vector RS = 8a + 20b. What does this show about PQ and RS?
- 15th August 1967A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 16th August 1967On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th August 1967Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 18th August 1967Write x^2 + 6x + 14 in the form (x + a)^2 + b.
- 19th August 1967A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 20th August 1967A cuboid measures 14 cm by 11 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st August 1967A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd August 1967A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 23rd August 1967A rectangle is 21 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th August 1967Work out the coordinates of the turning point of y = x^2 + 4x - 1.
- 25th August 1967y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 26th August 1967A cuboid measures 8 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th August 1967A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th August 1967On 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?
- 29th August 1967Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 30th August 1967Simplify (x^2 - 64)/(x - 8).
- 31st August 1967y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.