Daily Practice · Higher Plus
July 1967 5-a-day
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The batch download puts all 5 tiers' July 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1967Use the iteration x(n+1) = cube root of (11x(n) + 4) with x(0) = 1. Work out x(1) to 3 decimal places.
- 2nd July 1967A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd July 1967The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 4th July 1967A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 5th July 1967A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 6th July 1967Simplify sqrt(45) + sqrt(80), giving your answer in the form a sqrt(b).
- 7th July 1967Work out the nth term of the quadratic sequence 8, 18, 34, 56, ...
- 8th July 1967y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 9th July 1967In 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 July 1967The probability of winning a game is 1/2. A player expects 48 wins. How many games did they play?
- 11th July 1967On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th July 1967A rectangle is 24 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th July 1967The point (2, -6) lies on y = f(x). Write down its image on y = -f(x).
- 14th July 1967y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 15th July 1967In a vector proof you find that vector PQ = 6a + b and vector RS = 18a + 3b. What does this show about PQ and RS?
- 16th July 1967A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 17th July 1967A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 18th July 1967Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 19th July 1967Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 20th July 1967y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 64.
- 21st July 1967A cuboid measures 14 cm by 14 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd July 1967A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd July 1967On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th July 1967A block has mass 200 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th July 1967f(x) = 3x - 2 and g(x) = 4x - 8. Work out fg(0).
- 26th July 1967A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 27th July 1967A cuboid measures 5 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th July 1967A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th July 1967A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 30th July 1967x = 106 and y = 11, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st July 1967The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.