Daily Practice · Higher Plus
November 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1970 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1970y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 49.
- 2nd November 1970A cuboid measures 5 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd November 1970A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th November 1970On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th November 1970Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 6th November 1970Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 2. Work out x(1) to 3 decimal places.
- 7th November 1970A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 8th November 1970A cuboid measures 7 cm by 13 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th November 1970A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th November 1970A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 11th November 1970A rectangle is 13 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th November 1970Work out the nth term of the quadratic sequence -1, 12, 33, 62, ...
- 13th November 1970y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 14th November 1970The 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.
- 15th November 1970A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 16th November 1970On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th November 1970Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 18th November 1970The point (-5, -3) lies on y = f(x). Write down its image on y = f(-x).
- 19th November 1970y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 20th November 1970In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 21st November 1970The probability of winning a game is 2/5. A player expects 30 wins. How many games did they play?
- 22nd November 1970A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 23rd November 1970A block has mass 810 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th November 1970Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 25th November 1970y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 64.
- 26th November 1970In a vector proof you find that vector PQ = 6a - 2b and vector RS = 24a - 8b. What does this show about PQ and RS?
- 27th November 1970A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 28th November 1970On 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?
- 29th November 1970x = 72 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th November 1970f(x) = 6x - 2 and g(x) = 5x - 5. Work out fg(0).