Geometry and trigonometry Topic assessment 1. Describe fully the curve whose equation is [pic]. [2] 2. Show that the line y = 3x – 10 is a tangent to the circle [pic]. [4] 3.
Name Class Date 8-1 1. 3s3t3 Practice Adding and Subtracting Polynomials Form K Find the degree of each monomial. 2. 3n 3. 5xy 4.
The diagram below shows the graph of y = –x . 2 y O x (–3, k) y = –x2 The point (–3, k) lies on the graph. Find the value of k. 1 6. C B 12 cm A 1 1 In triangle ABC, AB = 12 centimetres, sin C = 2 and sin B = 3 . Find the length of side AC.
a) b) c) d) 16. Which equation represents the Objective Function for the above problem? a) b) c) d) 17. Write the equation of a square root graph that has been vertically compressed by a factor of , reflected over the x-axis, translated down 2 units and right 3 units. 18.
Note: I want the direction of the conventional current. 5. Consider the circuit in Figure 3, where R1 = 5.00×102Ω, R2 = 1.00×103Ω, and VB = 10.0V . (a) What is the equivalent resistance Req of the circuit? (b) Solve the circuit.
{ b = 2 + a } b) Multiplies b by 4 and stores the result in a. { a = b * 4} c) Divides a by 3.14 and stores the result in b. { b = a MOD 3.14 } d) Subtracts 8 from b and stores the result in a { a = 8 – b } 4. Assume the variables result, w, x, y and z are all integers, and that w=5, x=4, y=8 and z=2. What value will be stored in result in each of the following statements?
160.131 Mathematics for Business (1) Test 1 4th of April, 2012 Formulas you may need Slopes (Gradients) The slope (or gradient) m of a curve measures the rate of change in the dependent variable (y), i.e. m = [pic] = [pic] = [pic] = [pic] Determining the Equation of a Line: If we know 2 distinct points (x1, y1) and (x2, y2) on the line: y – y1 = [pic](x – x1); if we know a point (x0, y0) and the slope m of the line: y – y0 = m(x – x0); if we know the slope m and the y-intercept (0, c) of the line: y = mx + c. multiplier = - [pic] Inverse Matrices for 2 × 2 matrices: If A = [pic] then A-1 = [pic][pic], provided ad – bc [pic] 0. Best Fit Curves and
176 b. 352 c. 1936 d. 968 12. Solve: 28 = y – 4. a. y = 24 b. y = -32 c. y = -4 d. y = 32 13. Solve: 6y = 54. a. y= 9 b. y = 60 b. y = 48 d. y = 8 14. Evaluate: 4a + (a – b)³, when a = 5 and b = 2. a.
Name———————————————————————— Lesson 1.4 Date —— — — — — — — — — — — — Practice B For use with the lesson “Solve ax 2 + bx + c = 0 by Factoring” 1. 3x 2 1 10x 2 8 2. 2x 2 1 5x 2 3 3. 4x 2 1 4x 1 1 4. 2x 2 2 5x 1 1 5.
We can conclude that the data are Poisson distributed. Chi-Square test of independence Problem 12.12 Use the following contingency table to determine whether variable 1 is independent of variable 2. Let α = .01 | Variable 2 | Variable1 | 24 | 13 | 47 | 58 | | 93 | 59 | 187 | 244 | Step 1 Ho: the two classifications are independent Ha: the two classifications are dependent Step 2 d.f = (r – 1) (c – 1) Step 3 α = 0.01 x 2 0.01, 3df = 11.3449 Step 4 Reject Ho if x 2 > 11.3449 | Variable 2 | Total | Variable1 | 24 (22.92) | 13 (14.10) | 47 (45.83) | 58 (59.15) | 142 | | 93 (94.08) | 59 (57.90) | 187 (188.17) | 244 (242.85) | 583