Daily Practice · Higher Plus
November 1967 5-a-day
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The batch download puts all 5 tiers' November 1967 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1967A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 2nd November 1967A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 3rd November 1967Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 4th November 1967f(x) = 4x - 5 and g(x) = 6x + 6. Work out fg(-1).
- 5th November 1967y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 6th November 1967In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 7th November 1967The probability of winning a game is 7/8. A player expects 84 wins. How many games did they play?
- 8th November 1967On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th November 1967Simplify sqrt(72) + sqrt(50), giving your answer in the form a sqrt(b).
- 10th November 1967The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 11th November 1967y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 12th November 1967In a vector proof you find that vector PQ = 6a + 6b and vector RS = 18a + 18b. What does this show about PQ and RS?
- 13th November 1967A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 14th November 1967A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 15th November 1967A rectangle is 30 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th November 1967A quadratic sequence starts 16, 35, 64, 103. Work out the second difference, and the coefficient of n^2.
- 17th November 1967y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 18th November 1967A cuboid measures 14 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th November 1967A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th November 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?
- 21st November 1967Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 22nd November 1967Solve x^2 + 15x + 56 > 0.
- 23rd November 1967A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 24th November 1967A cuboid measures 9 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th November 1967A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th November 1967A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 27th November 1967A block has mass 520 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th November 1967Write x^2 - 10x + 14 in the form (x + a)^2 + b.
- 29th November 1967y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 30th November 1967The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.