Daily Practice · Higher Plus
January 1967 5-a-day
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The batch download puts all 5 tiers' January 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1967x = 43 and y = 32, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd January 1967f(x) = 4x - 5 and g(x) = 4x - 4. Work out fg(4).
- 3rd January 1967y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 4th January 1967The 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.
- 5th January 1967A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 6th January 1967A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 7th January 1967A car covers 730 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.
- 8th January 1967The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 9th January 1967y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 25.
- 10th January 1967In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 11th January 1967The probability of winning a game is 5/8. A player expects 60 wins. How many games did they play?
- 12th January 1967On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th January 1967Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 14th January 1967A quadratic sequence starts 8, 21, 42, 71. Work out the second difference, and the coefficient of n^2.
- 15th January 1967A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 16th January 1967In a vector proof you find that vector PQ = 3a - 4b and vector RS = 15a - 20b. What does this show about PQ and RS?
- 17th January 1967A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 18th January 1967A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 19th January 1967Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 20th January 1967Solve x^2 - 7x + 6 > 0.
- 21st January 1967y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 22nd January 1967A cuboid measures 4 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd January 1967A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th January 1967On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th January 1967A rectangle is 30 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th January 1967Write x^2 - 14x - 8 in the form (x + a)^2 + b.
- 27th January 1967y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 28th January 1967A cuboid measures 5 cm by 9 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th January 1967A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th January 1967A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 31st January 1967Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).